Accelerated Trading Models Used in Securities Class Action Lawsuits

McCann, Craig J., Hsu, David, Journal of Legal Economics

Experts have developed stock trading models to estimate total damages in securities class action lawsuits. The accelerated trading model is one such stock trading model. Stock trading models differ primarily in their assumptions about the frequency of shares retrading. Discussions of the accelerated trading model in the literature - and its application in expert testimony - often contain a critical error that results in several undesirable outcomes, including (1) an artificial cap on damaged shares regardless of the length of the class period or the amount of trading volume, (2) negative trading volume under real-world conditions, and (3) a turnover likelihood ratio that increases over time. Because of these flaws, previous versions of the accelerated trading model are poor tools for estimating damages.

Introduction

Damages in securities class action lawsuits depend on both the number of damaged shares and the damage per share. Shares are considered damaged if they are bought when the stock price is artificially high due to material omissions or misrepresentations and held until the fraud-related inflation is reduced or eliminated. Damage per share is the difference between the fraud-related inflation in the price at which the securities were bought and the fraud-related inflation when they were sold. The fraud-related inflation is usually assumed to be zero at the end of the class period.

An exact count of the plaintiffs' damages is not practical when a company @ s stock is held by thousands of investors. Therefore, stock trading models that estimate damages are extremely helpful to both sides in shaping strategy and evaluating settlement options. In this comment, we describe one typical model used to estimate the number of damaged shares in securities class actions, the accelerated trading model. We also illustrate and discuss the implications of an error that is commonly overlooked in the application of accelerated trading models.

Since membership in the plaintiff class typically is based upon stock purchases, a natural estimate ofthe number of shares potentially affected by the alleged fraud is the sum of the stock trading volume over the class period. However, given that the same share may be traded several times in a class period, total trading volume over the class period may exceed shares outstanding. It is difficult to determine the exact number of damaged shares in securities class actions because some shares purchased at artificially high prices are sold while prices are still artificially high; that is, these shares are retraded.

The simplest model for estimating damaged shares, the proportional trading model, was developed by the plaintiffs experts. The proportional trading model assumes that each share available to trade is equally likely to trade on any given day. This assumption implies that if a share traded yesterday, the probability that it will be retraded today is simply equal to the percent of the shares available to trade that traded today. For instance, if 100,000 shares were available to trade today and 1,000 shares traded, the model would assume that 1% of the shares that traded yesterday traded again today.

One alternative stock trading model is the accelerated trading model. The accelerated trading model assumes that the probability that a share which has already traded during the class period is retraded on a subsequent day in the class period is a constant multiple of the probability that a share which has not yet traded is traded for the first time. Some experts claim that the accelerated trading model is superior because its assumptions better reflect investor behavior than the proportional trading model t s assumptions. The accelerated trading model generally assumes more retrading of previously traded shares than the proportional trading model and therefore yields lower damages estimates.

Applications of the accelerated trading model in the literature and in expert testimony - assume that the probability that a share which has already traded during the class period is retraded on a subsequent day in the class period is a constant multiple of the probability that an average share is traded. …

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